On the asymptotic expansion of a ratio of gamma functions

212 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Selection Problems in the Presence of Implicit Bias (2018, unknown): “[20] Francesco Giacomo Tricomi and Arthur Erdélyi.”
Beta Processes, Stick-Breaking and Power Laws (2011, background): “(10) [cf. Tricomi and Erd´elyi, 1951]: Again, we see behavior in the form of a power law at work.”
Excess-Risk of Distributed Stochastic Learners (2013, unknown): “For this purpose, we call upon the following lemma from [36], [45], which describes some properties of the Gamma function.”
Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications (2016, methodology): “We have On the other hand, By collecting both estimates, we conclude that Recall the identity for the quotient of Gamma functions in [30, Section 7 (15)]: (5.1) valid for Re( β − α ) > 0, Re( z + α ) > 0.”
Fractional differential equations with dependence on the Caputo-Katugampola derivative (2016, unknown): “[19]), we have lim N→∞ Γ(N + 1− α) Γ(N + 1) = 0.”
On a Caputo-type fractional derivative (2018, unknown): “Similarly, taking the limit ρ → 0 and using the result (see [12]) Γ(z + α) Γ(z + β) ≈ z α−β as z →∞ and α, β ≥ 0, we obtain lim ρ→0 ( ∗D 0+ tβ)(x) = (CDα 0+ tβ)(x) = (ρ )ραxβ = βαxβ , that is, the new derivative coincides with the fractional derivative in the Caputo–Hadamard sense.”